A lower-bound on Mutual Information can be derived from an upper bound on \(\mathcal {H}[\hat{\theta }|\theta ]\)  for each \(\theta \)  – in other words, by upper-bounding the entropy of an estimator of the parameter \(\theta \) . For this, we draw inspiration from Stam's inequality [1]}, [2]}, [3]}, which states
\(\mathcal {H}[\hat{\theta }|\theta ] \le \frac{1}{2}\log \left|2\pi e \mathcal {F}(\theta )^{-1}\right| \, ,\) 
